Some results on the reverse order law in rings with involution (Q443935)

Let \(R\) be a unital ring with involution, let \(a^\sharp\) denote the group inverse of \(a\in R\), and let \(a^\dagger\) denote its Moore-Penrose inverse. Various characterizations of conditions such as \((ab)^\sharp = b^\dagger a^\dagger\) are obtained.